Undergraduate Research Project For some integer n, find an n-piece dissection of a regular pentagon to form a regular heptagon, making use of the dissections of Problems 12 and 15. (Hint: Remember to use the device of superimposing one dissection onto another; superimposed cut lines will create additional pieces in the dissection.)
NOTE: A famous theorem of geometry asserts that any two polygons having equal areas may be dissected into the same number of pairwise congruent triangles. Thus, for any two positive integers m and n (≥ 3), a regular m-gon may be cut into triangular pieces, which can be reassembled to form a regular n-gon. This theorem is due to J. Bolyai, one of the discoverers of hyperbolic geometry, discussed later in Chapter 6.
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